biomass co-firing under oxy-fuel conditions: a computational fluid...
TRANSCRIPT
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Biomass co-firing under oxy-fuel conditions: A computational fluid dynamics
modelling study and experimental validation
L. Álvarez1, C. Yin2, J. Riaza1, C. Pevida1, J.J. Pis1, F. Rubiera1*
1 Instituto Nacional del Carbón, INCAR-CSIC, Apartado 73, 33080 Oviedo, Spain
2 Department of Energy Technology, Aalborg University, 9220 Aalborg East, Denmark
Abstract
This paper presents an experimental and numerical study on co-firing olive waste (0,
10%, 20% on mass basis) with two coals in an entrained flow reactor under three oxy-
fuel conditions (21%O2/79%CO2, 30%O2/70%CO2 and 35%O2/65%CO2) and air-fuel
condition. Co-firing biomass with coal was found to have favorable synergy effects in
all the cases: it significantly improves the burnout while remarkably lowers NOx
emissions. The reduced peak temperatures during co-firing can also help to mitigate
deposition formation in real furnaces. Co-firing CO2-neutral biomass with coals under
oxy-fuel conditions can achieve a below-zero CO2 emission if the released CO2 is
captured and sequestered. The model-predicted burnout and gaseous emissions were
compared against the experimental results. A very good agreement was observed, the
differences in a range of ±5-10% of the experimental values, which indicates the model
can be used to aid in design and optimization of large-scale biomass co-firing under
oxy-fuel conditions.
Keywords: Biomass co-firing; Synergy effects; CO2 capture; Oxy-fuel combustion;
Below-zero CO2 emissions; CFD
* Corresponding Author: Tel : +34 985 119090; E-mail address: [email protected]. (F. Rubiera)
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1. Introduction
The combustion of coal in power plants generates a large amount of CO2 which is one
of the major contributors to global climate change. A diverse power generation portfolio
including Carbon Capture and Storage (CCS) technologies and renewable energies is
needed to reduce current atmospheric CO2 concentration of 393 ppm to below 354 ppm
in 1990. During oxy-coal combustion, coal is burnt in a mixture of oxygen and recycled
flue gas (mainly CO2 and H2O), to yield a rich stream of CO2 which, after purification
and compression, is ready for sequestration [1]. Co-firing biomass with fossil fuels in
existing utility boilers is also a feasible technology which can not only significantly
reduce CO2 emissions but also increase the share of renewable energy sources in energy
systems [2, 3]. The combination of oxy-coal combustion with biomass co-firing could
afford a way to increase CO2 capture efficiency [4]. Biomass co-firing has been
successfully performed in over 200 installations worldwide for a large number of
combinations of fuels, either in pilot tests or as part of commercial enterprises [5].
Though problems may arise in relation to biomass transport costs and difficulties in
milling, these can be manageable if adequate consideration is given to the fuels, design
and operating conditions used in the burners and boilers [6].
Compared with biomass co-firing, oxy-fuel combustion is still in the demonstration
stage, with plans for industrial scale-up to come into effect in the near future [4]. The
successful implementation of oxy-fuel combustion depends on fully understanding the
difficulties that can arise from replacing nitrogen by CO2 in the oxidizer stream. Oxy-
fuel conditions strongly promote radiative heat transfer, as a result of the much higher
levels of CO2, H2O, and in-flame soot, as well as the different CO2/H2O ratio to that of
air-firing combustion [7]. Other aspects of combustion, such as volatile combustion,
flame ignition and stability, or pollutant formation, may also be affected [8]. Biomass
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co-firing under oxy-fuel is likely to bring up more uncertainties. Biomass co-firing
under oxy-fuel conditions is an attractive option to simultaneously increase the use of
renewable energy sources, exploit the favorable synergy effects of biomass/coal co-
firing and achieve below-zero CO2 emissions, which has been very little investigated so
far [9-12]. For instance Smart et al. [11] evaluated the impact of co-firing biomass on
pollutant formation, burnout and heat transfer under oxy-fuel conditions in a 0.5 MWt
combustion test facility. Experiments at laboratory scale have been focused on the
effects of different co-firing ratios on burnout and NO emissions [12].
Computational Fluid Dynamics (CFD) models have been used to simulate pulverised
coal and biomass co-firing in conventional combustion systems [13-15]. In recent years,
on the basis of the accumulated knowledge of the fundamental differences between air-
fuel and oxy-fuel combustion, much effort has been devoted to developing and
validating sub-models for the new combustion environment. For instance, new
approaches have been developed for heat transfer modelling in environments with high
concentrations of CO2 and H2O vapor, e.g., the Weighted-Sum-of-Gray-Gases-Model
(WSGGM) refined for oxy-fuel combustion modelling [16, 17]. Specific models for
volatile combustion in CO2–rich environments [18] and for char combustion under oxy-
fuel conditions [19] have also been developed. In terms of modelling of biomass co-
firing under oxy-fuel conditions, a recent paper by Holtmeyer at al. [20] could be the
only effort in literature, in which the effect of co-firing sawdust and a subbituminous
coal on NO emissions in air and oxy-fuel conditions was studied.
This paper is to comprehensively study co-firing biomass with coals under air-fuel and
oxy-fuel conditions in a lab-scale entrained flow reactor (EFR). The computational fluid
dynamics (CFD) study is the main workhorse and the experimental study is used to
validate the CFD modelling. Among others, the effects of biomass shares in co-firing
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(from 0 to 20 wt% of biomass), firing conditions, and different coals to be separately
used in co-firing on the overall combustion behavior and NO emissions are investigated
and discussed.
2. Experimental setup
All the combustion experiments of this study were performed in a down-fired EFR,
which has been introduced in detail in Riaza et al. [21]. Figure 1 shows a schematic
diagram of the reactor. The EFR has an internal diameter of 4 cm and a length of 200
cm. For the experiments reported in this work a reaction zone of 140 cm was used. The
EFR was electrically heated and the preheated gases were introduced through flow
straighteners to ensure laminar flow conditions. The experiments were performed at a
heated furnace temperature of 1273 K. The gas flow was set to 22.4 L/min, which
corresponds to a residence time of 2.5 s. The amount of excess oxygen in the oxidant
over the required stoichiometric oxygen was set to %25,2 =exO . The excess oxygen was
then used to calculate the required fuel mass flow rate, )1/( ex,2st, Omm FF += && , where
st,Fm& represents the stoichiometric fuel mass flow rate. Four different combustion
atmospheres were employed: air (21%O2/79%N2), and three binary gas mixtures of O2
and CO2 (21%O2/79%CO2, 30%O2/70%CO2 and 35%O2/65%CO2).
- Figure 1 here -
Two coals of different rank were used in this work: a semi-anthracite from the Hullera
Vasco-Leonesa in León, Spain (HVN); and a South African high-volatile bituminous
coal from the Aboño power plant (350 MWe) in Asturias, Spain (SAB). A biomass,
olive waste (OW) was also employed. This biomass is the solid waste that remains after
the process of pressing and extraction of olive oil. The coal and biomass samples were
ground and sieved to obtain a particle size fraction of 75-150 μm. The proximate and
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ultimate analyses together with the high heating values of the fuel samples are presented
in Table 1.
- Table 1 here -
The fuel samples in a hopper were fed into the EFR reaction zone through a cooled
injector. The fuel particles were then injected into the centre of the preheated gas
stream. The reaction products were quenched by aspiration in a stream of nitrogen by
means of a water-cooled probe. The particles were removed by means of a cyclone and
a filter, and the coal burnout was determined by the ash tracer method. The exhaust
gases were monitored using a battery of analyzers Emerson X-Stream X2GP with non-
dispersive infrared photometers detectors for CO, CO2, SO2, and NO; and a
paramagnetic sensor for O2.
The experimental findings on burnout (defined in this study as the ratio of mass loss of
a fuel sample during its combustion to the original mass of the fuel feed) and NO
emissions have been reported in a previous paper on experimental study [12]. Here, the
results were used to validate the CFD simulations, in order to evaluate the effect of
biomass co-firing on burnout and NO emissions under various conditions and to
establish the modelling capability for oxy-fuel combustion of biomass/coal blends.
3. Numerical modelling
When solid fuel particles are injected into the reactor, some interdependent processes
(e.g., gas and particle phase dynamics, turbulence, heat transfer, pollutants formation,
and homogenous and heterogeneous reactions) take place and need to be appropriately
taken into account in modelling. In this study, the simulations were performed using a
commercial CFD package, Ansys Fluent version 13 [22]. Most of the principal
equations of the combustion sub-models were explained in detail in the Fluent Theory
Guide. Here, only the user-defined submodels (i.e., for oxy-coal radiation) or the
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significant reactions and their kinetics which are very dependent on fuel and operation
conditions (i.e., char and volatile combustion or fuel devolatilisation), are described in
detail. Details of the mesh and boundary conditions are also given.
Because of the symmetrical conditions at two perpendicular mid-planes, only a quarter
of the total reaction zone of the EFR (4 cm i.d., 140 cm height) was used in the
simulations. The simulation domain was meshed into a high-quality structured grid
consisting of about 75,000 hexahedral cells, which was same as that used in our
previous oxy-coal combustion study [23]. The mesh was found fine enough to assure
grid-independent simulation results. Totally 24 different combustion tests were
performed in our experimental study, i.e., six different fuel samples or blends under four
atmospheres, respectively. Table 2 shows in detail the share of biomass (on mass basis)
in the fuel blend, feeding rate of the blend, composition and mass flowrate of the
gaseous reactant into the reactor for each of the test cases. The temperature of the
reactor wall and the injector wall was 1273 K and 373 K, respectively. All the 24 test
cases were numerically simulated here.
- Table 2 here -
3.1. Gas and particle phase dynamics
Transport equations for the continuous phase were solved using an Eulerian approach
and the fuel particles were tracked in a Lagrangian frame of reference through the
calculated gas field. The trajectories of solid fuel particles were computed using the
discrete phase model, by assuming spherical particles and retaining only the drag and
gravity forces in the equation of motion of the particles. The effect of turbulence was
accounted for by the RNG k-ε turbulence model. Although this model was developed
and mainly used for high-Reynolds number turbulent flows, the use of a differential
equation for turbulent viscosity, which is derived from the scale elimination procedure
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in RNG theory, also enables the model to better and successfully handle low-Reynolds
number and near-wall flows [22, 24, 25]. The size distribution of the coal particles was
fitted to a Rosin-Rammler distribution. The minimum, mean and maximum particle
diameters are 75, 115 and 150 µm, respectively. The spread parameter is unity and 5
size groups are considered. The effect of turbulence on particle dispersion was taken
into account using the discrete random walk model. Totally 2400 particle streams are
tracked in each case.
Here it has to be mentioned that in this study both the tracking and conversion of
biomass particles were modelled in the same methodology as coal particles. In general,
biomass particles are often fibrous and non-friable. Therefore, biomass particles
prepared and used for suspension co-firing are often much larger in size and more
irregular in shape than pulverized coal particles. Yin et al. [13] developed a model to
track large, nonspherical particles in fluid flows, which was validated using their
experimental results of the motion of a large cylindrical particle (length of 50 mm and
aspect ratio of about 9) in a water flow and then applied to biomass/natural gas co-firing
modelling. They also extended their efforts to large biomass particle conversion by
accounting for various intra-particle processes in modelling and found for pulverized
biomass particles of a few hundred microns in diameters the intra-particle heat and mass
transfer was a secondary issue at most in particle conversion under suspension-firing
conditions [26, 27]. Gubba et al. [28] developed a model to evaluate the influence of
particle shape and internal thermal gradients on biomass suspension co-firing flames. In
this study, the biomass particles are tiny in size (below 200 μm) and near-spherical in
shape. Under the conditions of all the test cases, the Biot number is well below 0.1, i.e.,
1.0/Bi 61 <<⋅≡ kdh p , where h , pd and k represent convection heat transfer coefficient
between the gas and solid fuel particle, diameter of solid fuel particle, and heat
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conductivity of solid fuel particle, respectively. So the particles can be considered to be
under isothermal conditions. This is also in line with the conclusion that isothermal
particle assumption may be no longer valid when the pulverised particle size exceeds
150-200 μm [29]. The biomass particles are assumed to be spherical, so only the gravity
and the standard drag force were retained in the equation of motion for biomass
particles, which is the same way used for coal particle tracking in this study.
3.2. Coal and biomass devolatilisation
In this study the devolatilisation rate of the solid fuels was modelled using a single step
first-order Arrhenius equation. For both the coals, the pre-exponential factor (A) and
activation energy (Ea) were obtained by means of the FG-DVC (Functional Group-
Depolymerisation Vaporation Crosslinking) code [30], and the values were estimated
assuming a final temperature of 1273 K and a heating rate of 105 K/s. For the biomass,
the kinetic values of A and Ea were obtained from an extensive review paper on biomass
pyrolysis [31]. Table 3 summarizes the kinetic data used as the devolatilisation model
inputs in the modelling study.
- Table 3 here -
It is necessary to point out that the FG-DVC predictions were determined for an inert
atmosphere. The release rate of the volatiles was not remarkably affected by the high
CO2 concentrations [32], although in the later stages of combustion there may be a
certain degree of char gasification with CO2. In a previous work of Álvarez et al. [33],
comparison of coal devolatilisation in N2 and CO2 atmospheres was conducted in a
thermogravimetric apparatus. Before devolatilisation was finished at around 1150 K, the
mass loss curves in the N2 and CO2 atmospheres followed a similar trend. The
additional mass loss in the CO2 atmosphere above 1173 K, when the release of volatiles
had already finished, was mainly due to the char-CO2 reaction. Thus, we employed the
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same devolatilisation kinetics for the air- and oxy-firing CFD simulations. Then a char-
CO2 reaction was included in the char combustion sub-model.
3.3. Volatile combustion
During the different conversion processes of fuel particles along their trajectories, some
species are released into gas phase (e.g., volatiles and CO), creating sources for gas
phase combustion. The volatiles often carry a large percentage of the energy of solid
fuels (e.g., about 50% for coals and an overwhelming majority for biomass). The
homogeneous combustion of the volatiles also plays a vital role in ignition and flame
stability, local temperature, species distribution and pollutant formation. Moreover, high
CO2 concentration under oxy-fuel conditions may also affect the gas-phase combustion.
Therefore, gas-phase combustion mechanism is expected to play an important role in
modelling of the co-firing processes. To describe the gas composition in the EFR, the
species transport approach was used, with the Eddy-Dissipation Concept for the
turbulence-chemistry interaction. In the CFD simulations, the volatile gases were
lumped into one single “artificial” species, CHyOx. The compositions and the formation
enthalpies were determined from the proximate and ultimate analyses of the fuels. The
lumped volatiles were represented by CH3.87O0.11, CH3.56O0.47 and CH2.45O0.93, and their
formation enthalpies (in J/kmol) were -4.2×107, -5.4×108 and -4.0×108 for the HVN,
SAB and OW, respectively. For the air combustion cases, six species were defined as
follows: CHyOx, O2, H2O, CO, CO2 and N2, and the original Jones and Lindstedt 4-step
(JL-4) global mechanism [34], was employed:
CHyOx + (0.5+0.25y –0.5x)O2 → CO + 0.5y H2O (R1)
CO+ 0.5 O2 → CO2 (R2)
CO + H2O → CO2 + H2 (R3)
H2 + 0.5 O2 → H2O (R4)
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For oxy-coal combustion cases, CO2 was set as the last species and a refined JL-4
mechanism with the kinetics adapted for oxy-fuel combustion conditions was employed
[18]. In comparison with the original JL-4 step mechanism, the refined JL-4 mechanism
retains the initiating reactions involving hydrocarbon and O2 (R1), whilst refines the
CO-CO2 reactions (R2) in order to improve prediction of major species concentration.
The refined JL 4-step mechanism was also implemented in CFD modelling of a 0.8 MW
oxy-natural gas flame, and both the predicted gas species (e.g., CO2, O2, CO and H2)
and gas temperature showed a good agreement with experimental results [35].
3.4. Char oxidation
For char oxidation, the multiple-surface-reaction char model was employed. At the
temperatures of this EFR, CO is the dominant product in char oxidation C(s) +O2 →
CO/CO2. Therefore, only the reaction (R5) was considered in char oxidation modelling.
The CO formed in (R5) will undergo further reactions as shown in (R2) and (R3).
C(s) + 0.5 O2 → CO (R5)
Global kinetics for the coal char combustion rates, represented as Arrhenius
expressions, were based on the activation energies and pre-exponential factors as
determined by Gil et al. [36], as summarized in Table 4.
- Table 4 here -
At the temperature of this work (1273 K), combustion takes place in Regime II (kinetics
and diffusion control). The effectiveness factor (η), defined as the ratio of the diffusion
rate to the maximum diffusion rate, is a measure of the extent of penetration of the
oxidant into the char matrix. It was determined via the Thiele modulus as calculated by
Gharebaghi et al. [19] for a large number of defined oxy-fuel combustion cases. At
elevated temperature and CO2 concentrations, char CO2 gasification could become more
important particularly in the later stages of the oxy-fuel combustion process. As long as
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the oxygen concentration is higher, the contribution of the gasification reactions will be
much smaller than that of the oxidation reactions. Nevertheless, char gasification was
also considered in the modelling study (R6), and its kinetic data was obtained from the
literature [37, 38]. In the current simulations, the effect of CO2 gasification reaction
accounted for less than 1% on coal burnout.
C(s) + CO2 → 2CO (R6)
The combustion of biomass char is more complicated since it is affected not only by the
composition of the biomass, but also by the shape and size of the particle. Different
approaches can be found in literature, such as the diffusion-limited surface reaction rate
model modified by the aspect ratio-dependent enhancement factor [13], or Smith’s
intrinsic model modified by a constant enhancement of 4 to represent the higher burning
rate of the biomass char particles [14]. In this study, both the raw biomass particles and
the resulting biomass char particles are near-spherical and the carbon content in the
biomass is relatively low (about 20%). Therefore, no special enhancement factor was
used for biomass char oxidation. The kinetics for biomass char combustion were
obtained from [39, 40].
3.5. Heat transfer model
In a pulverised fuel chamber, radiation is often the dominant mode of heat transfer. The
most widely used model for gaseous radiative properties is the Weighted-Sum-of-Gray-
Gases-Model (WSGGM), which represents a reasonable compromise between an
oversimplified gray gas model and a comprehensive approach addressing high-
resolution dependency of radiative properties and intensity upon wavelength. The model
parameters derived by Smith et al. [41] for several partial pressures of CO2 and H2O
vapor in typical air-fuel combustion are often used in combustion modelling. The
original Smith et al. WSGGM is a one-clear-gas, three-gray-gas model. However, it is
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often implemented in a further simplified way in which constant properties over the
entire spectrum are assumed and only one single radiative transfer equation per
direction is solved for the entire spectrum, e.g., as implemented in Ansys Fluent.
Recently, some efforts are made to refine and extend the WSGGM for oxy-fuel
conditions. For instance, Yin et al. [16] used the exponential wide band model, the same
reference model as Smith et al. used in their derivation, to generate a much broader
emissivity database covering also oxy-fuel conditions, and derived new WSGGM
parameters by using an improved data-fitting technique. The refined WSGGM also
included more representative conditions to better account for the variations in H2O/CO2
molar ratio in an oxy-fuel flame. The importance of nongray-gas effects in modelling of
large-scale oxy-fuel combustion was also well demonstrated and nongray calculation of
an appropriate WSGGM was highly recommended for combustion modelling [42].
In this study, the Discrete Ordinates model was employed for radiative transfer equation
for both oxy- and air-fuel combustion. In the oxy-fuel combustion modelling, non-gray
calculation of the oxy-fuel WSGGM [16] was performed to evaluate the gaseous
radiative properties. Compared to the conventional gray calculation of the Smith et al.
air-fuel WSGGM, it does not remarkably compromise computational efficiency while
has inherent potentials to improve simulations of oxy-fuel combustion processes, in
which the degree of improvement depends on the scale or the beam length of the
furnace under study. For the simulations in the oxy-fuel atmosphere with the highest
CO2 content (i.e., 21% O2/79% CO2) non-gray oxyfuel WSGGM and gray air-fuel
WSGGM calculations were both performed. Since the reactor under simulation is small
(in terms of beam length), using new gaseous radiation properties led to little
differences in CFD predictions, just as expected. The deviations in temperature profiles
for both cases were less than ±1%.
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3.6. NOx formation
NOX simulations were carried out as a post-processor. For air-firing conditions, both the
thermal and fuel-NO were considered. For oxy-firing conditions, fuel-NO formation
was considered to be the dominant mechanism.
Fuel-NO is formed from the oxidation of molecular nitrogen organically bound within
the fuel mass. Fuel-bound nitrogen can either be released during devolatilisation
(referred to as volatile-N), or can remain in the char (referred to as char-N). The
partitioning of nitrogen between char and volatiles, summarized in Table 5, was
determined experimentally. Usually, it is assumed that HCN and NH3 are the dominant
species formed as nitrogen-bearing intermediates at rates that depend both on the local
combustion conditions and on the nitrogen content of each specific fuel [43]. For
biomass, it was assumed that NH3 was the only nitrogen intermediate, whereas for coals
the HCN and NH3 release rates were based on the prediction made by Álvarez et al. [44]
HCN and NH3 are competitively oxidised and reduced to form NO and N2, respectively,
according to DeSoete’s scheme:
HCN + O2 → NO + … RTOHCN eXXR /95.280451
210101 −⋅⋅⋅⋅= (1/s) (R7)
HCN + NO → N2 + ... RTNOHCN eXXR /25115112103 −⋅⋅⋅⋅= (1/s) (R8)
NH3 + O2 → NO + ... RTONH eXXR /2.133947
236104 −⋅⋅⋅⋅= (1/s) (R9)
NH3 + NO → N2 + ... RTNONH eXXR /95.113017
38108.1 −⋅⋅⋅⋅= (1/s) (R10)
where HCNR& , 3NHR& , X , uR and T represent the conversion rate of HCN (1/s),
conversion rate of NH3 (1/s), molar fraction, universal gas constant (=8.315 J/(mol·K)),
and gas temperature (K), respectively.
The fuel nitrogen partitioning between the char and the volatiles can be estimated by
pyrolysis network codes, obtained from the literature or determined experimentally. In
this work, the partitioning of the fuel-bound nitrogen between the char and volatiles was
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determined experimentally during the devolatilisation of the samples in N2 and CO2 in
the EFR at 1273 K. From the analysis of N content of the parent samples and that of the
chars, and using the ash as a tracer method, the char and char-N yields can be
determined and, thus, the nitrogen content in char and volatiles was estimated. Char-N
was assumed to be heterogeneously oxidised to NO, for both coal and biomass char
particles, with an assumed conversion factor of 20% (mass/mass %) [45].
- Table 5 here –
4. Results and discussion
4.1. Overall combustion behaviour
In biomass combustion, the higher volatile yields produce more off-gas, which causes
the off-gas to proceed to a much larger volume in the reactor before mixing with the
oxidizer and completing gas-phase combustion. Therefore, biomass flame tends to
occupy a much larger flame volume (i.e., the regions with low O2 and high CO
concentration) than coal flame [27, 28]. The large flame volume effectively evens out
the temperature distribution and lowers the peak temperatures, which favors a lower
pollutant formation (e.g., lower NOx emission) and a reduced deposition potential. The
comparatively low (relative to the peak temperature in a coal flame, still high enough)
and uniform temperature distribution in a much larger flame volume also favors a
higher burnout. Both improved burnout and decreased NOx emissions were observed in
this study when the coals were co-fired with biomass under different operating mode.
Table 6 shows a comparison between the experimental and predicted burnouts. A very
good agreement can be observed, in which the difference between the experimental
results and model predictions fell within a range of ±5-10% of the experimental values
for all the test cases.
- Table 6 here -
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As can be seen from Table 6, co-firing biomass led to a noticeable increase in the
burnout for both coals. This effect became more pronounced as the biomass share
increased, especially in the atmospheres with a lower O2 content, i.e., 21%O2/79%N2
and 21%O2/79%CO2. For the HVN-OW blends, there was a great improvement in the
burnout, especially when switching from 10% to 20 wt% of biomass addition.
Comparatively, the improvement was not so obvious for the SAB-OW blends, since the
individual coal SAB had already reached a high burnout degree before being blended
with the biomass and there was less margin for improvement. Table 6 also shows the
predicted burnouts very well reproduce the trend observed in experiments, indicating
that the CFD model successfully describes the co-firing behaviour in the air and oxy-
fuel conditions.
More details about the co-firing characteristics under various conditions in the EFR can
be revealed from the CFD modelling study. Figure 2 shows the temperature contours in
the mid plane of the EFR for both its whole length and its first 40 cm, during HVN-OW
co-firing under different conditions, whereas Figure 3 shows the local fluctuations in the
area-weighted average temperature profiles around the location where the solid fuel
stream is ignited. In all cases the devolatilisation of the fuels takes place after the
injection of the fuel (at a distance of 0.15 m from the top of the reactor) and there is an
increase in temperature due to the heat released during the combustion of the volatiles.
Significant differences can be observed between the 21%O2/79%N2 and the
21%O2/79%CO2 atmosphere. When N2 is replaced by CO2, the gas temperatures drop
significantly due to the higher specific molar heat of CO2. It can also be observed that to
obtain similar gas temperatures in oxy-firing conditions to those of air-firing, the
oxygen content in the CO2 mixture must be of the order of ~30-35% to counteract the
negative effect of the higher CO2 heat capacity. Increasing the O2 percentage in CO2 up
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to 30 or 35% is still insufficient to match the heat capacity of the air. However, under
the 30%O2/70%CO2 and 35%O2/65%CO2 atmospheres, the increase in the mass flux
rate (cf. Table 2) promotes the consumption rate of the volatiles, providing extra heat
feedback to the fuel particles and leading to higher gas and particle temperatures.
- Figs. 2 and 3 here -
Figure 2 shows the temperature distribution in the EFR. As expected, the addition of
biomass made some difference in the gas temperature distribution. Co-firing biomass
with coal tends to even out the high-temperature zones into a larger volume but with
decreased peak temperatures, especially under oxy-fuel conditions, which leads to a
higher burnout and a lower emission. This observation is in line with the findings in
literature. For instance, Molcan et al. [46] carried out biomass/coal co-firing
experiments in a 3 MWth combustion test facility, and found that biomass addition to
coal not only improved combustion efficiency but also led to lower flame temperatures.
Yin et al. [28] performed simulations for coal and straw combustion in a swirl-stabilized
burner, and in the case of the straw-flame the gas temperature predictions were slightly
lower than for the coal-flame. Ma et el. [14] also performed a numerical study for co-
firing coal and biomass, and their predictions (as well as the experimental values)
showed that the addition of biomass (wood, Miscanthus and olive waste) to coal would
result in a decrease in gas temperatures.
Figure 4 shows the counterpart for SAB-OW co-firing under various conditions: the
temperature contours in the mid plane of the EFR for both its whole length and its first
40 cm, whereas Figure 5 shows the evolution of the area-weighted temperature of the
gases with axial location. The similar tendency as in HVN-OW co-firing can also be
observed here.
- Figs. 4 and 5 here -
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Figures 6 and 7 show the burning rates in air and oxy-firing conditions during the HVN-
OW co-firing and SAB-OW co-firing, respectively. For both blends, differences in
combustion behaviour under air and oxy-fuel conditions are apparent. When the co-
firing condition is switched from air-fuel (i.e., 21%O2/79%N2) to low O2 concentration
oxy-fuel (i.e., 21%O2/79%CO2), the overall gas temperature level drops significantly,
which leads to a reduced burnout (as seen in Table 6). When increasing O2
concentrations in the oxy-fuel conditions (e.g., 30%O2/70%CO2 and 35%O2/65%CO2),
an increase in the burning rate is observed, because of the increased temperature levels
and the increased oxidizer concentration. This, in turn, gives rise to a higher burnout, as
shown in Table 6.
- Figs. 6 and 7 here -
4.2. NOx emissions
Table 6 shows a comparison between the experimental and predicted NO emissions for
all the test cases. A very good agreement between the experimental and predicted results
is achieved.
SAB and HVN have very similar nitrogen contents: 1.8% vs. 1.7% on dry basis.
However, the burnout in SAB/OW co-firing is obviously higher than HVN/OW co-
firing for all the OW shares (from 0 to 20% on mass basis), meaning a higher char-N
conversion to NO in the former. As a result, SAB-OW co-firing is expected to produce
higher NO emission than HVN-OW co-firing. However, NO emission from SAB-OW
co-firing was found to be lower than that from HVN-OW co-firing in almost all the test
cases. One of the explanations is the much higher volatiles in SAB, which are released
and burned in the lower part of the EFR and serve as a re-burning agent to reduce the
formed NO to N2. The higher amount of NH3 and HCN released may also favour the
reduction of the formed NO to N2 via reactions (R8) and (R10).
18
For both the coals, NO concentration decreases when they are co-fired with biomass in
all the test conditions, even though the biomass has similar nitrogen content than both
the coals. The reduced peak temperatures during co-firing are one of the reasons for the
decreased NO emission. The large amount of off-gas released from the biomass may
proceed to a larger volume in the EFR prior to mixing with oxidizer and burnout. The
reducing atmosphere in part of the reactor favours the reduction of the NO formed to
N2. Comparatively, the decrease in NO emission from SAB-OW co-firing is more
remarkable than that from HVN-OW co-firing, thanks to the much higher volatile
content in SAB.
- Figs. 8 and 9 here -
Figures 8 and 9 show more details of the predicted NO concentration profiles in the mid
plane of the EFR during HVN-OW co-firing and SAB-OW co-firing, respectively. A
decrease in NO emissions is observed when switching from conventional air-firing
condition to 21%O2/79%CO2 oxy-firing condition, mainly because of the decreased
temperature levels. NO emissions will increase monotonously as O2 concentrations in
the oxy-firing conditions increases (e.g., to 30% or 35%).
5. Conclusions
A comprehensive experimental and numerical study on co-firing olive waste with two
coals of different rank in a laboratory scale entrained flow reactor at 1273 K under
conventional air-fuel condition and three oxyfuel conditions was undertaken. Favorable
synergy effects were observed in the co-firing tests: co-firing biomass with coal not
only improved burnout but also reduced NOx emissions. The CFD-predicted burnout
and gaseous emissions were compared against the experimental results. A very good
agreement was achieved for all the cases: the differences between experimental and
modelling results fell in a range of ±5-10% of the experimental values, indicating a
19
good potential of the modeling routine for large-scale biomass co-firing under oxy-fuel
conditions.
Acknowledgements
L.A. acknowledges funding from the CSIC JAE program, co-financed by the European
Social Fund. J.R. acknowledges funding from the Government of the Principado de
Asturias (Severo Ochoa program). Financial support from the CSIC (Project PIE
201080E09) is gratefully acknowledged.
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Table 1. Proximate and ultimate analyses of the samples used in this work
Sample OW HVN SAB Origin Spain Spain S. Africa Rank sa hvb Proximate analysis (wt %)Moisture 9.0 1.1 2.4 Volatile matter (db) 71.9 9.2 29.9 Ash (db) 7.6 10.7 15.0 Fixed carbona (db) 20.5 80.1 55.1 Ultimate analysis (wt %, db)C 50.2 81.9 69.3 H 6.1 3.1 4.2 N 1.8 1.7 1.8 S 0.2 1.4 0.8 Oa 34.1 1.2 8.9 High heating value (MJ/kg, db) 19.9 31.8 27.8 sa: semi-anthracite; hvb: high-volatile bituminous coal.
db: dry basis.
a Calculated by difference.
26
Table 2. Inputs of the CFD code for the gases and coal and biomass blends feed rates
Atmosphere Gas inlet
(g/min)
Coal and biomass blends mass flow rate (g/min)
HVN-OW blends SAB-OW blends
0%OW 10%OW 20%OW 0%OW 10%OW 20%OW
21%O2/79%N2 1.548 0.110 0.114 0.119 0.105 0.135 0.139
21%O2/79%CO2 2.118 0.110 0.114 0.119 0.105 0.135 0.139
30%O2/70%CO2 2.058 0.157 0.164 0.171 0.147 0.194 0.196
35%O2/65%CO2 2.016 0.182 0.190 0.198 0.175 0.225 0.231
27
Table 3. Devolatilisation data inputs for the CFD code
Sample A (s-1) Ead (kJ mol-1)
OW 1.9×109 127.0
HVN 3.60×1014 229.7
SAB 4.68×1011 155.9
28
Table 4. Char combustion kinetic parameters employed
Coal Char obtained in N2 Char obtained in CO2
A (s-1) Ead (kJ mol-1) A (s-1) Ead (kJ mol-1)
OW 1×108 89.4 - -
HVN 5.09×104 127 8.10×103 117
SAB 9.48×104 120 2.31×105 125
29
Table 5. Nitrogen content (%mass) in char and volatiles after coal devolatilisation in the EFR in N2 and CO2
Coal Char obtained in N2 Char obtained in CO2
N-char N-volatile N-char N-volatile
OW 2.25 1.57 2.11 1.67
HVN 1.93 1.94 1.90 2.31
SAB 2.38 2.64 2.26 2.70
30
Table 6. Experimental and predicted burnouts and NO emissions for HVN-OW and SAB-OW combustion in air and oxy-fuel atmospheres (21-35% O2)
Burnout
(%)
21%O2/79%N2 21%O2/79%CO2 30%O2/70%CO2 35%O2/65%CO2
Exp Pred Exp Pred Exp Pred Exp Pred
HVN 79.5 79.5 77.1 77.1 81.0 80.8 82.9 82.3
90HVN-10OW 80.5 80.6 79.5 78.5 83.3 84.3 85.4 86.7
80HVN-20OW 83.0 84.0 81.1 81.0 83.9 84.0 85.9 85.6
SAB 92.5 92.3 90.2 89.7 93.9 92.7 94.7 94.6
90SAB-10OW 93.9 93.5 92.7 91.4 95.0 94.9 95.7 95.0
80SAB-20OW 95.2 94.3 93.0 93.1 95.8 95.6 97.8 95.7
NO emissions
(ppm)
21%O2/79%N2 21%O2/79%CO2 30%O2/70%CO2 35%O2/65%CO2
Exp Pred Exp Pred Exp Pred Exp Pred
HVN 384 390 360 362 578 573 626 613
90HVN-10OW 392 398 346 350 547 542 633 585
80HVN-20OW 395 390 339 343 548 551 633 578
SAB 400 388 359 360 498 504 474 527
90SAB-10OW 333 346 290 295 418 430 436 422
80SAB-20OW 270 293 181 237 330 340 350 354
31
Figure captions
Fig. 1. Schematic diagram of the entrained flow reactor (EFR)
Fig. 2. Predicted temperature (K) in the EFR when co-firing HVN-OW in (a)
21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively.
Fig. 3. Predicted area-weighted average temperature during combustion in air and
oxy-fuel environments of HVN-OW blends.
oxy-fuel atmospheres
Fig. 4. Predicted temperature (K) in the EFR when co-firing SAB-OW in (a)
21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively.
Fig. 5. Predicted area-weighted temperature during combustion in air and oxy-fuel
environments of blends SAB-OW.
Fig. 6. Predicted burning rate (kg/s) in the EFR when co-firing HVN-OW in (a)
21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively.
Fig. 7. Predicted burning rate (kg/s) in the EFR when co-firing SAB-OW in (a)
21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively.
Fig. 8. Predicted NO concentration (ppm) in the EFR when co-firing HVN-OW in (a)
21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively.
Fig. 9. Predicted NO concentration (ppm9 in the EFR when co-firing SAB-OW in (a)
21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively.
32
N2
Gas cylinders
Cooled injector
Feeding system
Samplingprobe
Cyclone
O2
CO
CO2
Mass flowcontrollers
Gas analysers
To vent
Filter
Pre -heater
Reaction tube
O2 CO2
NO
SO2
N2
Gas cylinders
Cooled injector
Feeding system
Samplingprobe
Cyclone
O2
CO
CO2
Mass flowcontrollers
Gas analysers
To vent
Filter
Pre -heater
Reaction tube
O2 CO2
NO
SO2
Figure 1. Schematic diagram of the entrained flow reactor (EFR).
33
80HVN
Tempe
rature (K
)
HVN 90HVN
a) b)
Tempe
rature (K
)HVN 90HVN 80HVN
Tempe
rature (K
)
HVN
c)
90HVN 80HVN 90HVN 80HVN
d)
HVN
Tempe
rature (K
)80HVN
Tempe
rature (K
)
HVN 90HVN
a)
80HVN
Tempe
rature (K
)
HVN 90HVN
a)Tempe
rature (K
)
HVN 90HVN
Tempe
rature (K
)
HVN HVN HVN 90HVN
a) b)
Tempe
rature (K
)HVN 90HVN 80HVN
b)
Tempe
rature (K
)HVN 90HVN 80HVN
Tempe
rature (K
)HVN 90HVN 80HVNHVN 90HVNHVN 90HVN 80HVN
Tempe
rature (K
)
HVN
c)
90HVN 80HVN
Tempe
rature (K
)
HVN
c)
90HVN
Tempe
rature (K
)
HVN
c)
Tempe
rature (K
)
HVN
Tempe
rature (K
)
HVN
c)
90HVN90HVN 80HVN 90HVN 80HVN
d)
HVN
Tempe
rature (K
)
90HVN 80HVN
d)
HVN
Tempe
rature (K
)d)
HVN
Tempe
rature (K
)
HVNHVN
Tempe
rature (K
)
Figure 2. Predicted temperature (K) in the EFR when co-firing HVN-OW in (a)
21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively
34
21%O2/79%N2
1000
1100
1200
1300
1400
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Distance (m)
Tem
pera
ture
(K)
HVN
90HVN-10OW
80HVN-20OW
21%O2/79%CO2
1000
1100
1200
1300
1400
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Distance (m)Te
mpe
ratu
re (K
)
HVN
90HVN-10OW
80HVN-20OW
30%O2/70%CO2
1000
1100
1200
1300
1400
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Distance (m)
Tem
pera
ture
(K)
HVN
90HVN-10OW
80HVN-20OW
35%O2/65%CO2
1000
1100
1200
1300
1400
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Distance (m)
Tem
pera
ture
(K)
HVN
90HVN-10OW
80HVN-20OW
Figure 3. Predicted area-weighted temperature during combustion in air and oxy-fuel
environments of HVN-OW blends.
35
Tempe
rature (K
)
SAB
Tempe
rature (K
)
b)
90SAB 80SAB
a)
90SABSAB
Tempe
rature (K
)
80SAB
SAB
c)
90SAB 80SAB 80SABSAB
Tempe
rature (K
)d)
90SAB
Tempe
rature (K
)
SAB
Tempe
rature (K
)
b)
90SAB 80SAB
a)
90SABSAB
Tempe
rature (K
)
80SAB
SAB
c)
90SAB 80SAB 80SABSAB
Tempe
rature (K
)d)
90SAB
SAB
Tempe
rature (K
)
b)
90SAB 80SAB
a)
90SABSAB
Tempe
rature (K
)
80SAB
SAB
c)
90SAB 80SAB
SAB
Tempe
rature (K
)
b)
90SAB 80SABSAB
Tempe
rature (K
)
b)
90SABSAB
Tempe
rature (K
)
b)
SAB
Tempe
rature (K
)
b)
SAB
Tempe
rature (K
)
SAB
Tempe
rature (K
)
b)
90SAB 80SAB
a)
90SABSAB
Tempe
rature (K
)
80SAB
SAB
c)
90SAB 80SAB
a)
90SABSAB
Tempe
rature (K
)
80SAB
a)
90SABSAB
Tempe
rature (K
)
80SAB90SABSAB
Tempe
rature (K
)
80SABSAB
Tempe
rature (K
)
SAB
Tempe
rature (K
)
80SAB80SAB
SAB
c)
90SAB 80SABSAB
c)
90SABSAB
c)
SAB
c)c)
90SAB 80SAB 80SABSAB
Tempe
rature (K
)d)
90SAB 80SABSAB
Tempe
rature (K
)d)
90SABSAB
Tempe
rature (K
)d)
90SAB
Tempe
rature (K
)d)
90SAB
Figure 4. Predicted temperature (K) in the EFR when co-firing SAB-OW in (a)
21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively.
36
21%O2/79%N2
1000
1100
1200
1300
1400
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Distance (m)
Tem
pera
ture
(K)
SAB
90SAB-10OW
80SAB-20OW
21%O2/79%CO2
1000
1100
1200
1300
1400
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Distance (m)
Tem
pera
ture
(K)
SAB
90SAB-10OW
80SAB-20OW
30%O2/70%CO2
1000
1100
1200
1300
1400
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Distance (m)
Tem
pera
ture
(K)
SAB
90SAB-10OW
80SAB-20OW
35%O2/65%CO2
1000
1100
1200
1300
1400
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Distance (m)
Tem
pera
ture
(K)
SAB
90SAB-10OW
80SAB-20OW
Figure 5. Predicted area-weighted temperature during combustion in air and oxy-fuel
environments of blends SAB-OW.
37
Burning rate (kg/s)
HVN
b)
90HVN 80HVN
Burning rate (kg/s)
HVN
a)
80HVN90HVN
HVN
Burning rate (kg/s)
c)
80HVN90HVN HVN
Burning rate (kg/s)
d)
80HVN90HVN
Burning rate (kg/s)
HVN
b)
90HVN 80HVN
Burning rate (kg/s)
HVN
b)
90HVN
Burning rate (kg/s)
HVN
b)
Burning rate (kg/s)
HVN
b)
HVNHVN
b)
90HVN 80HVN
Burning rate (kg/s)
HVN
a)
80HVN90HVN
Burning rate (kg/s)
HVN
a)
Burning rate (kg/s)
HVN
a)
HVN
a)
80HVN80HVN90HVN90HVN
HVN
Burning rate (kg/s)
c)
80HVN90HVNHVN
Burning rate (kg/s)
c)
HVN
Burning rate (kg/s)
HVNHVN
Burning rate (kg/s)
c)
80HVN80HVN90HVN90HVN HVN
Burning rate (kg/s)
d)
80HVN90HVNHVN
Burning rate (kg/s)
d)
HVN
Burning rate (kg/s)
HVNHVN
Burning rate (kg/s)
d)
80HVN80HVN90HVN
Figure 6. Predicted burning rate (kg/s) in the EFR when co-firing HVN-OW in (a)
21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively.
38
SAB 80SAB
d)
Burning rate (kg/s)
90SAB80SABSAB
Burning rate (kg/s)
c)
90SAB
80SABSAB
Burning rate (kg/s)
a)
90SABBu
rning rate (kg/s)
80SABSAB
b)
90SAB
SAB 80SAB
d)
Burning rate (kg/s)
90SABSAB 80SAB
d)
Burning rate (kg/s)
90SAB 80SAB
d)
Burning rate (kg/s)
90SAB
d)
Burning rate (kg/s)
90SAB
d)
Burning rate (kg/s)
d)
Burning rate (kg/s)
90SAB80SABSAB
Burning rate (kg/s)
c)
90SAB 80SAB80SABSAB
Burning rate (kg/s)
c)
90SABSAB
Burning rate (kg/s)
c)
SAB
Burning rate (kg/s)
c)
90SAB90SAB
80SABSAB
Burning rate (kg/s)
a)
90SAB 80SABSAB
Burning rate (kg/s)
a)
90SABSAB
Burning rate (kg/s)
a)
90SABSAB
Burning rate (kg/s)
a)
SAB
Burning rate (kg/s)
SAB
Burning rate (kg/s)
a)
90SABBu
rning rate (kg/s)
80SABSAB
b)
90SABBu
rning rate (kg/s)
80SABSAB
b)
90SAB 80SABSAB
b)
90SABSAB
b)
90SABSAB
b)
90SABSAB
b)
SABSAB
b)
90SAB
Figure 7. Predicted burning rate (kg/s) in the EFR when co-firing SAB-OW in (a)
21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively.
39
80HVN90HVNHVN
NO (p
pm)
d)
HVN
NO (p
pm)
a)
80HVN HVNNO (p
pm)
b)
90HVN 80HVN
HVN
NO (p
pm)
c)
90HVN80HVN
90HVN
80HVN90HVNHVN
NO (p
pm)
d)
HVN
NO (p
pm)
a)
80HVN HVNNO (p
pm)
b)
90HVN 80HVN
HVN
NO (p
pm)
c)
90HVN80HVN 80HVN90HVNHVN
NO (p
pm)
d)
80HVN90HVNHVN
NO (p
pm)
d)
90HVNHVN
NO (p
pm)
d)
HVN
NO (p
pm)
HVNHVN
NO (p
pm)
d)
HVN
NO (p
pm)
a)
80HVNHVN
NO (p
pm)
a)
HVN
NO (p
pm)
a)
HVN
NO (p
pm)
HVNHVN
NO (p
pm)
a)
80HVN HVNNO (p
pm)
b)
90HVN 80HVNHVNNO (p
pm)
b)
90HVNHVNNO (p
pm)
b)
HVNNO (p
pm)
HVNHVNNO (p
pm)
b)
90HVN 80HVN
HVN
NO (p
pm)
c)
90HVN80HVNHVN
NO (p
pm)
c)
90HVNHVN
NO (p
pm)
c)
HVN
NO (p
pm)
HVNHVN
NO (p
pm)
c)
90HVN80HVN
90HVN
Figure 8. Predicted NO concentration (ppm) in the EFR when co-firing HVN-OW in
(a) 21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively.
40
NO (p
pm)
SAB
NO (p
pm)
d)
90SAB 80SAB
SAB
NO (p
pm)
b)
90SAB 80SAB
a)
SAB 90SAB 80SAB
80SABSAB
NO (p
pm)
c)
90SAB
NO (p
pm)
SAB
NO (p
pm)
d)
90SAB 80SAB
SAB
NO (p
pm)
b)
90SAB 80SAB
a)
SAB 90SAB 80SAB
80SABSAB
NO (p
pm)
c)
90SAB SAB
NO (p
pm)
d)
90SAB 80SABSAB
NO (p
pm)
d)
90SABSAB
NO (p
pm)
d)
SAB
NO (p
pm)
SABSAB
NO (p
pm)
d)
90SAB 80SAB
SAB
NO (p
pm)
b)
90SAB 80SABSAB
NO (p
pm)
b)
90SABSAB
NO (p
pm)
b)
SAB
NO (p
pm)
SAB
NO (p
pm)
b)
90SAB 80SAB
a)
SAB 90SAB 80SAB
80SABSAB
NO (p
pm)
c)
90SAB
a)
SAB 90SAB 80SAB
a)
SAB 90SAB
a)a)
SAB 90SAB 80SAB
80SABSAB
NO (p
pm)
c)
90SAB 80SABSAB
NO (p
pm)
c)
90SABSAB
NO (p
pm)
c)
SAB
NO (p
pm)
SABSAB
NO (p
pm)
c)
90SAB
Figure 9. Predicted NO concentration (ppm) in the EFR when co-firing SAB-OW in
(a) 21%O2/79%N2, (b) 21%O2/79%CO2, (c) 30%O2/70%CO2 and (d) 35%O2/65%CO2.
Length scale is 140 cm and 40 cm respectively.